According to work energy thereom, the work done on the car to accelerate is,
[tex]W=\frac{1}{2}mv^2-\frac{1}{2}mu^2[/tex]Plug in the known values,
[tex]\begin{gathered} W=\frac{1}{2}(1200kg)(100km/h)^2(\frac{1000\text{ m}}{1\text{ km}})^2(\frac{1\text{ h}}{3600\text{ s}})^2(\frac{1\text{ J}}{1kgm^2s^{-2}})-_{}\frac{1}{2}(1200kg)(30km/h)^2(\frac{1000\text{ m}}{1\text{ km}})^2(\frac{1\text{ h}}{3600\text{ s}})^2(\frac{1\text{ J}}{1kgm^2s^{-2}}) \\ =462963\text{ J-}41667\text{ J} \\ =421296\text{ J} \end{gathered}[/tex]The power output of the engine can be given as,
[tex]P=\frac{W}{t}[/tex]Substitute the values,
[tex]\begin{gathered} P=\frac{421296\text{ J}}{10\text{ s}}(\frac{1\text{ W}}{1\text{ J/s}}) \\ =42129.6\text{ W} \end{gathered}[/tex]Therefore, the power output of the engine is 42129.6 W.
